In certain applications, such as medical optical image formation applications making it possible to restore images of the human body or industrial optical image formation for the non-destructive control of parts, recourse is made to image reconstruction techniques.
These image reconstructions are made from projections obtained by a transmitting acquisition device and capturing an irradiation radiation. These projections are obtained following a series of measurements for measuring the attenuation of the radiation through the object to be controlled, the incidence of the radiation having been modified between each series of measurements.
The acquisition devices are constituted by an X or .gamma. radiations source or neutrons source. They also comprise one or several detectors.
When there is only one detector, the source moves linearly and transmits at each movement so as to obtain a projection from a series of measurements; the geometry of the acquisition device is called parallel.
When there is a bar of detectors, the source is fixed, the measurement series is obtained from a single transmission and the acquisition geometry is called fan-shaped.
In the presence of a matrix of detectors, the geometry is known as conical.
Generally speaking, the objective is to have a large number of projections so as to obtain the best possible restoration of images of the object thus traversed by the radiation. In order to achieve this, the source is made to turn by small increments of angles around the object so as to obtain series of measurments under different incidences.
Generally speaking, the reconstruction of images (bidimensional images) from projections calls upon two major categories of methods:
the category of analytic methods, PA0 the category of algebraic methods. PA0 Reproduction (or projection) is an operation which, from an image or volume, makes it possible to obtain the projections relating to these spaces within a given geometry. PA0 Retroprojection (or spreading) is the dual processing of reprojection. It consists of redistributing the information derived from projections to the image pixels (or to volume voxels) belonging to an acquisition straight line. PA0 parallel, PA0 fan-shaped (constant linear pitch or constant angular pitch) PA0 conical (3-D). PA0 determining the index letter associated with the coordinate on the axis F of the corresponding point of the known space by taking the entire part ADR of the generalized expression a.sub.0 (e) with ##EQU1## e being the iteration index letter corresponding to the coordinate on the axis E of the point in question of the unknown space and V1, V2, V3 and V4 being constant parameters in the elementary phase, all these parameters being determined prior to this phase according to the selected acquisition geometry; and according to the type of operation (reprojection or retroprojection) carried out and the monodimensional units in question, PA0 determining the contribution C to be given to the numerical value of the point in question of the unknown space by interpolation on the numerical values of the corresponding ADR index point and possibly of adjacent points, PA0 weighting this contribution by a factor f determined by the following equation: ##EQU2## V5, V6 and V7 being constant parameters in the elementary phase, all these parameters being determined prior to this phase accrording to the selected acquisition geometry, the type of operation and the monodimensional sets in question, PA0 adding this weighted contribution to the numerical value of the relevant point of the unknown space determined during the preceding elementary phases which placed the point of the unknown space in correspondence with points of other known monodimensional spaces, all the contributions obtained at the end of the method to determine the unknown space thus constituting the final value of this point. PA0 m fixed at 0, n at n.sub.0, j at j.sub.0, k at 0, l.sub.0 (i) is sought EQU V3=1 EQU V4=0 EQU V1=h.sub.1 (n.sub.0, j.sub.0) EQU V2=.DELTA.L.sub.1 (j.sub.0) EQU e=i PA0 or PA0 m fixed at 0, l at l.sub.0, j at j.sub.0, k at 0; n.sub.0 (i) is sought EQU V3=1 EQU V4=0 EQU V1=h.sub.2 (l.sub.0, j.sub.0) EQU V2=.DELTA.L.sub.2 (j.sub.0) EQU e=i PA0 the terms h.sub.1, h.sub.2, .DELTA.L.sub.1 and .DELTA.L.sub.2 being predetermined and n.sub.0 and l.sub.0 are real numbers of respectively the entire part n and l. PA0 k=0, m=0, n=n.sub.0, j=j.sub.0, l.sub.0 (i) being sought, EQU V1=h.sub.3 (j.sub.0, n.sub.0) EQU V2=h.sub.4 (n.sub.0) EQU V3=h.sub.5 (j.sub.0, n.sub.0) EQU V4=h.sub.6 (n.sub.0) EQU e=i PA0 or: k=0, m=0, n=n.sub.0, i=i.sub.0, l.sub.0 (j) being sought, EQU V1=h'.sub.3 (i.sub.0, n.sub.0) EQU V2=h'.sub.4 (n.sub.0) EQU V3=h'.sub.5 (i.sub.0, n.sub.0) EQU V4=h'.sub.6 (n.sub.0) EQU e=j. PA0 the terms h.sub.3, h.sub.4, h.sub.5, h.sub.6, h'.sub.3, h'.sub.4, h'.sub.5, h'.sub.6 being predetermined and l.sub.0 is a real number of the entire part l. PA0 m fixed at 0, n at n.sub.0, j at j.sub.0, k at 0, l.sub.0 (i) being sought, EQU V1=h.sub.7 (n.sub.0, j.sub.0) EQU V2=h.sub.8 (n.sub.0, j.sub.0) EQU V3=h.sub.9 (j.sub.0) EQU V4=h.sub.10 (j.sub.0) EQU e=i PA0 or: PA0 m fixed at 0, l at l.sub.0, j at j.sub.0, k at 0, n.sub.0 (i) being sought, EQU V1=h'.sub.7 (l.sub.0, j.sub.0) EQU V2=h'.sub.8 (l.sub.0, j.sub.0) EQU V3=h'.sub.9 (j.sub.0) EQU V3=h'.sub.10 (j.sub.0) EQU e=i PA0 V5 predetermined on the basis of the parameters of the acquisition device EQU V6=V3 EQU V7=V4. PA0 address generation means receiving the parameters V1 to V4 delivering the address ADR which is the entire part of a.sub.0 (e); PA0 means to store the numerical values of the points of the known space addressed by the generation means delivering the set of (.alpha.+1) numerical values of the points of the known space from V(ADR-.beta.) to V(ADR+.gamma.) (.beta. and .gamma. being positive integers; .beta.+.gamma.=.alpha.) corresponding to the index ADR, .alpha. being the order of interpolation; PA0 weighting means receiving each non-weighted contribution and the parameters V5, V6 and V7 to deliver each weighted contribution; PA0 addition means to add to the numerical value of the current point of the unknown space the weighted contribution relating to this current point; PA0 storage means containing the current value. PA0 address generation means receiving the parameters V1 to V4 delivering the address ADR which is the entire section a.sub.0 (e); these same address generation means also provide the addresses of the elements of the unknown space; PA0 means to store the numerical values of the points of the known space and the numerical values of the points of the unknown space addressed by the address generation means, thus delivering the numerical values of the known space from V(ADR-.beta.) to V(ADR+.gamma.) (.beta. and .gamma. being positive integers; .beta.+.gamma.=.alpha.) corresponding to the index ADR, .alpha. being the order of interpolation, thus delivering the numerical values of the data of the unknown space corresponding to the calculations carried out and receiving the numerical values of the unknown space after processing; PA0 an operative unit receiving the coefficients for interpolation, receiving the parameters V5, V6 and V7 so as to weight the contribution and add it to the value of the point during processing of the unknown space, these operations being carried out intrinsically to this operative unit. PA0 a first stage consisting of a parallel geometry bidimensional reprojection making it possible to obtain the RADON transform; PA0 a second stage consisting of a parallel geometry bidimensional retroprojection making it possible to obtain rearranged projections; PA0 a third stage consisting of a parallel geometry bidimensional retroprojection making it possible to obtain the sought-after final volume .
The analysis of these analytic and algebraic methods shows that, apart from filtering, rearrangement, masking operations, etc., the basic operations are reprojection and retroprojection.
In the case of the optical image formation x, each point of the projection corresponds to an estimate of the energy attenuation of a beam of X-rays on a linear path in space regarded as supposed to be known.
This reprojection operation is especially used in iterative techniques (algebraic method) and in certain volume reconstruction methods by synthesis and inversion of the RADON transform.
It is possible to refer to the thesis of P. Grangeat held at the Ecole Nationale Superieure des Telecommunications and dated Jun. 30, 1987 and entitled "Analysis of a 3D optical image formation system by reconstruction from conical geometry X-rays". Reference may also be made to the patent application FR8707134 published under the No 2615619.
This operation is used in all reconstruction (images or volumes) methods from projections. As part especially of analytic methods, it is sometimes associated with data rearrangement and filtering operations.
These two operations (reprojection and retroprojection) are strictly linked with the geometry of the acquisition system which has generated the initial data. This geometry, as said earlier, may be:
The data volume to be processed and the complexity of reconstruction methods thus constitute a problem requiring the use of high-performing processing means.
The most natural solution, which consists of using non-dedicated (standard) vectorial processors to implement these methods, results in having a high price/performance ratio. This solution provides a certain amount of flexibility (as they are frequently programmable in an evolved language), but this occurs to the detriment of price and performance.
In addition, these currently exists a certain number of specific machines. Specific bidimensional retroprojection processors have been produced as part of tomographic systems. For example, the STAR Technology company distributes a retroprojector (fan-shaped geometry) associated with a vectorial processor.
By virtue of their conception, all products currently existing on the market are linked to an acquisition geometry and as a result have not been designed to allow for the efficient implementation of reprojection and retroprojection operations as regards the various geometries.
It is to be noted that the methods making it possible to carry out reprojections and retroprojections are characterized by a set of imbricated iterative phases: phase concerning the projections--phase solely concerning image planes in 3D cases--phase concerning image-lines--phase concerning the elements of the line--and the phase concerning the projections may be imbricated anywhere prior to the element phase.
The lowest level phase concerns the correspondence of the line elements and is qualified as an elementary phase. This phase places in correspondence two monodimensional units (which can be assimilated to lines), one of which is known. The operations incident to this phase make it possible to calculate a contribution to each element of the unknown monodimensional unit. This phase is repeated by about N.sup.3 (respectively about N.sup.4 times) at the time of reconstructuring an image of size N.sup.2 (respectively with a size volume N.sup.3) from N projections.